TY - JOUR
T1 - Analysis of the Implicit-Explicit Ultra-Weak Discontinuous Galerkin Method for Convection-Diffusion Problems
AU - Wang , Haijin
AU - Xu , Anping
AU - Tao , Qi
JO - Journal of Computational Mathematics
VL - 1
SP - 1
EP - 23
PY - 2023
DA - 2023/12
SN - 42
DO - http://doi.org/10.4208/jcm.2202-m2021-0290
UR - https://global-sci.org/intro/article_detail/jcm/22150.html
KW - The ultra-weak discontinuous Galerkin method, Convection-diffusion, Implicit-explicit time discretization, Stability, Error estimate.
AB - <p style="text-align: justify;">In this paper, we first present the optimal error estimates of the semi-discrete ultra-weak
discontinuous Galerkin method for solving one-dimensional linear convection-diffusion equations. Then, coupling with a kind of Runge-Kutta type implicit-explicit time discretization
which treats the convection term explicitly and the diffusion term implicitly, we analyze
the stability and error estimates of the corresponding fully discrete schemes. The fully
discrete schemes are proved to be stable if the time-step $\tau ≤ \tau_0,$ where $\tau_0$ is a constant independent of the mesh-size $h.$ Furthermore, by the aid of a special projection and a careful
estimate for the convection term, the optimal error estimate is also obtained for the third
order fully discrete scheme. Numerical experiments are displayed to verify the theoretical
results.</p>